A364742 - OEIS

%I #12 Aug 05 2023 10:32:36

%S 1,1,4,13,50,201,841,3627,15993,71803,327082,1508002,7023446,32995626,

%T 156173668,744029238,3565030063,17169013899,83061503584,403483653745,

%U 1967217524551,9623463731721,47220968518786,232354408276613,1146254897566224,5668118931395946

%N G.f. satisfies A(x) = 1 / (1 - x*(1 + x*A(x))^3).

%H Seiichi Manyama, <a href="/A364742/b364742.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = (1/(n+1)) * Sum_{k=0..n} binomial(n+1,k) * binomial(3*k,n-k).

%o (PARI) a(n) = sum(k=0, n, binomial(n+1, k)*binomial(3*k, n-k))/(n+1);

%Y Cf. A001006, A161634, A364743, A364744.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Aug 05 2023